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<h1>Modeling</h1>
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<h1>Introduction</h1>
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<p>Three kinds of enzymes are needed to turn cellulose into glucose.
Enzymes Exoglucanase and Endoglucanase are placed in bottom layer of
bioflim, and β-glucosidase are in layer 2. layer 3 could be used to
further degrade glucose to further degraded molecule such as alcohols.
Our application is a combination of stratified bioflim and
bio-conversion of celluloses which is a part of the project of Team
Edinburgh of igem 2011. Therefore their model (with matlab) could be
used to describe our system with some adjustment.</p>
<p><img src="sugarfilm-background-1.jpg" / width="690"/></p>
<p>&nbsp;</p>
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<h1>Basic concepts and assumptions</h1>
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<p>Based on the results of former sections, the expression of
proteins in the bottom layer and middle layer are determined by only
factor of time, and they would become a constant after the system
reached a steady-state. Thus we could set the concentration of these
three enzymes to be two constants E_1 and E_2, where Exoglucanase and
Endoglucanase are of same concentration C_1 in bottom layer, and
concentration of β-glucosidase is C_2 in layer 2. Team Edinburgh has
already built a matlab based model in their igem 2011 project for free
floating enzyme approach in simulating conversion of celluloses. Their
method could be applied in our model. Assumptions of their models are
listed below.</p>
<p>1 Underlying assumption: cellulose, cellobiose, and glucose
concentrations change continuously with time. <br />
2 Rate equations assume enzyme adsorption follows the Langmuir isotherm
model. <br />
3 Glucose and cellobiose, which are the products of cellulose
hydrolysis, are assumed to "competitively inhibit enzyme hydrolysis". <br />
4 All reactions are assumed to follow the same temperature dependency
Arrhenius relationship (shown below). However, in reality it should be
different for every enzyme component, "because of their varying degrees
of thermostability, with β-glucocidase being the most thermostable.
Hence the assumption is a simplification of reality". <br />
5 Conversion of cellobiose to glucose follows the Michaelis-Menten
enzyme kinetic model. <br />
6 Concentration of xylose is assumed to be zero all the time for
simplify. <br />
7 Diffusion is assumed to be linear. That is, the concentration of
cellobiose in layer 2 is assumed to be a constant times c (assumed to be
0.6) its concentration in layer 1. <br />
8 The temperature of the system is a constant. (30℃) <br />
9 Concentration of celluloses in middle layer is assumed to be zero (no
diffusion). <br />
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<p>Cellulose to cellobiose reaction with competitive glucose and cellobiose inhibition in bottom layer.</p>
<img src="http://igem.org/wiki/images/d/d7/Zmodeling2.png" />
<p>Cellulose to glucose reaction with competitive glucose and cellobiose inhibition in bottom layer.</p>
<img src="http://igem.org/wiki/images/1/14/Zmodeling3.png" />
<p>Cellobiose to glucose reaction with competitive glucose and cellibiose inhibition in bottom layer.</p>
<img src="http://igem.org/wiki/images/a/a3/Zmodeling4.png" />
<p>Cellobiose to glucose reaction with competitive glucose and cellibiose inhibition in middle layer.</p>
<img src="http://igem.org/wiki/images/5/59/Zmodeling5.png" />
<p>The Langmuir Isotherm model mathematically describes enzyme adsorption onto solid cellulose substrates.</p>
<img src="http://igem.org/wiki/images/3/34/Zmodeling6.png" />
<p>Cellulose mass balance in bottom layer</p>
<img src="http://igem.org/wiki/images/8/89/Zmodeling7.png" />
<p>Cellobiose mass balance in bottom layer</p>
<img src="http://igem.org/wiki/images/9/9e/Zmodeling8.png" />
<p>Glucose mass balance in bottom layer</p>
<img src="http://igem.org/wiki/images/b/b2/Zmodeling9.png" />
<p>Glucose production in middle layer</p>
<img src="http://igem.org/wiki/images/f/f6/Zmodeling10.png" "/>
<p>Overall glucose production is equal to g+G.</p>
<p>Overall glucose production is equal to g+G.</p>

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<h1>Parameters</h1>
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<p>In bottom layer, we set E_1 to be 1g/kg, E_2 to be 0.01g/kg, and
concentration of cellulose to be 100g/kg. Without considering the
reaction in middle layer, the concentrations in bottom layer are shown
in following graph.</p>

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<div id="banner_list"><a href="#" target="_blank"><img
	src="http://2011.igem.org/wiki/images/2/22/Zmodeling11k.png" title=""
	alt="In bottom layer, we set E_1 to be 1g/kg, E_2 to be 0.01g/kg, and concentration of cellulose to be 100g/kg. Without considering the reaction in middle layer, the concentrations in bottom layer are shown in following graph."
	width="570" height="430" /></a> <a href="#" target="_blank"><img
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<h1>References</h1>
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<p>[1] Team Edinburgh 2011. “Modeling(Matlab)” iGEM wiki. <br />
[2] Kadam KL, Rydholm EC, McMillan JD (2004) Development and Validation
of a Kinetic Model for Enzymatic Saccharification of Lignocellulosic
Biomass. Biotechnology Progress 20(3): P 698–705</p>
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